Geodesic
Solvability of certain inverse problems for the nonstationary kinetic transport equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 9, pp. 1622-1627 Cet article a éte moissonné depuis la source Math-Net.Ru

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Linear and nonlinear inverse problems for the nonstationary multispeed anisotropic kinetic transport equation are studied. Sufficient conditions for the existence and uniqueness of weak solutions to these problems in various function spaces are found. The proofs of the corresponding theorems imply that solutions of the inverse problems under study can be obtained by applying the method of successive approximations. 
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N. P. Volkov. Solvability of certain inverse problems for the nonstationary kinetic transport equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 9, pp. 1622-1627. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_9_a7/

[1] Marchuk G. I., Metody rascheta yadernykh reaktorov, Atomizdat, M., 1961

[2] Tikhonov A. N., Arsenin V. Ya., Timonov A. A., Matematicheskie zadachi kompyuternoi tomografii, Nauka, M., 1987

[3] Germogenova T. A., Lokalnye svoistva reshenii uravneniya perenosa, Nauka, M., 1986

[4] Agoshkov V. I., Obobschennye resheniya uravneniya perenosa i svoistva ikh gladkosti, Nauka, M., 1988

[5] Vladimirov V. S., “Osobennosti resheniya uravneniya perenosa”, Zh. vychis. matem. i matem. fiz., 8:4 (1968), 189–202

[6] Kuznetsov Yu. A., Morozov S. F., “Korrektnost postanovki smeshannoi zadachi dlya nestatsionarnogo uravneniya perenosa”, Differents. ur-niya, 8:9 (1972), 1639–1648 | MR | Zbl

[7] Marchuk G. I., “O postanovke nekotorykh obratnykh zadach”, Dokl. AN SSSR, 156:3 (1964), 503–506 | MR | Zbl

[8] Maslennikov M. V., “Problema Milna s anizotropnym rasseyaniem”, Tr. MIAN SSSR, 97, 1968, 3–133

[9] Anikonov D. S., “Ob obratnykh zadachakh dlya uravneniya perenosa”, Differents. ur-niya, 2:1 (1974), 7–17

[10] Anikonov D. S., “Mnogomernye obratnye zadachi dlya uravneniya perenosa”, Differents. ur-niya, 20:5 (1984), 817–824 | MR | Zbl

[11] Sultangazin U. N., Irkegulov I. Sh., “O nekotorykh obratnykh zadachakh atmosfernoi optiki”, Nekorrektnye zadachi matem. fiz. i analiza, Nauka, Novosibirsk, 1984, 143–149 | MR

[12] Anikonov D. S., Prokhorov V. I., “Neobkhodimye i dostatochnye usloviya edinstvennosti resheniya odnoi zadachi tomografii”, Zh. vychisl. matem. i matem. fiz., 30:8 (1990), 1262–1267 | MR

[13] Gryn V. I., “Ob obratnykh zadachakh statsionarnogo perenosa”, Zh. vychisl. matem. i matem. fiz., 34:11 (1994), 1831–1853

[14] Anikonov Yu. E., “Obratnye zadachi dlya kineticheskikh uravnenii”, Uslovno-korrektnye zadachi matem. fiz. i analiza, Nauka, Novosibirsk, 1992, 26–41

[15] Prilepko A. I., Ivankov A. L., “Obratnye zadachi opredeleniya koeffitsienta i pravoi chasti nestatsionarnogo mnogoskorostnogo uravneniya perenosa po pereopredeleniyu v tochke”, Differents. ur-niya, 21:1 (1985), 109–119 | MR | Zbl

[16] Prilepko A. I., Ivankov A. L., “Obratnye zadachi opredeleniya koeffitsienta, indikatrisy rasseyaniya i pravoi chasti nestatsionarnogo mnogoskorostnogo uravneniya perenosa”, Differents. ur-niya, 21:5 (1985), 870–885 | MR | Zbl

[17] Prilepko A. I., Volkov N. P., “Obratnye zadachi opredeleniya parametrov nestatsionarnogo uravneniya perenosa po pereopredeleniyam integralnogo tipa”, Differents. ur-niya, 23:1 (1987), 124–136 | MR | Zbl

[18] Prilepko A. I., Volkov N. P., “Obratnye zadachi opredeleniya parametrov nestatsionarnogo kineticheskogo uravneniya perenosa po dopolnitelnoi informatsii o sledakh iskomoi funktsii”, Differents. ur-niya, 24:1 (1988), 136–146 | MR | Zbl

[19] Prilepko A. I., Ivankov A. L., Volkov N. P., “O nekotorykh obratnykh zadachakh teorii nestatsionarnogo perenosa”, Uspekhi matem. nauk, 41:4 (1986), 156–157

[20] Volkov N. P., “On some inverse problems for time-dependent transport equation”, ILL-Posed Problems in Natural Sciences, TVP-VSP, M., 1992, 431–438 | MR